This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A365447 #38 Jul 23 2025 16:04:58
%S A365447 1,3,189,26254935,392654823152462915625,
%T A365447 28032331438680332717218961936012273854096893310546875
%N A365447 Number of nonempty choice functions on a set of n alternatives.
%C A365447 Number of choice functions f:2^A\{{}}->2^A\{{}} where A is an n-element set of variants such that f(X) is a nonempty subset of any nonempty X in 2^A (here 2^A denotes the power set of A).
%D A365447 F. Aleskerov, D. Bouyssou, and B. Monjardet, Utility, Maximization, Choice and Preference, Springer, 2007, pp. 28-31.
%H A365447 Dmitry I. Ignatov, <a href="https://ceur-ws.org/Vol-3489/paper5.pdf">A Note on Counting Basic Choice Functions with Formal Concept Analysis</a>, FCA4AI@IJCAI 2023, 47-56.
%F A365447 a(n) = Product_{k=1..n} (2^k-1)^binomial(n, k).
%F A365447 log_2 a(n) = n*2^(n-1) + O(2^n/sqrt(n)).
%e A365447 a(1) = 1 since 2^{1} = {{}, {1}} and there exists only one function f:2^{1}/{{}}->2^{1}/{{}} satisfying f(X) is a nonempty subset of any nonempty X in 2^A, i.e., f({1})={1}.
%t A365447 a[n_] := Product[(2^k - 1)^Binomial[n, k], {k, 1, n}]; Array[a, 6] (* _Amiram Eldar_, Oct 03 2023 *)
%Y A365447 Cf. A061301, A229333.
%K A365447 nonn,easy
%O A365447 1,2
%A A365447 _Dmitry I. Ignatov_, Oct 03 2023